It is known to measure the altitude and the vertical speed of an aircraft, for example of a rotary wing aircraft, with the aid of barometric capsules which carry out barometric measurements. However, such barometric measurements which are accurate at high altitude exhibit considerable errors at low altitude, especially in the case of a rotary wing aircraft, such as a helicopter for example, by virtue of the existence of a ground effect specified hereinbelow.
It is known that the lift of a helicopter is based on the equality between the thrust of the main rotor and the weight of the helicopter. Normally, in particular at high altitude, the discontinuity in pressure encountered in an air jet passing through the disk of the main rotor consists essentially of a pressure reduction on the suction surface, this not disturbing the operation of a barometric capsule intended for measuring the barometric altitude, whose static-pressure taps are arranged on the fuselage of the helicopter, that is to say at the level of the pressure surface. However, at low altitude [for example at an altitude of less than 18 meters (60 feet)], the flow of the air stream interacts with the ground and an overpressure is created under the disk of the main rotor giving rise to the above-indicated ground effect. In this case, the levitating force is of course still the same, but the new equilibrium is based almost entirely on the overpressure prevailing between the rotor disk and the ground. By virtue of the considerable size of a helicopter main rotor, the entire fuselage is situated in this overpressure field and hence also the static-pressure taps of a barometric capsule, thereby giving rise to a considerable error during the measurement of the barometric altitude by means of such a barometric capsule. A similar error appears in the measurement, at low altitude, of the barometric vertical speed, that is to say of the vertical speed of the aircraft which is based on a barometric measurement.
In order to at least partially remedy these drawbacks, it is known to use a value of vertical acceleration which is measured by an attitude and heading unit of the aircraft, so as to filter (and hence correct) the barometric altitude measurement used during the estimation of the vertical speed and/or of the altitude of an aircraft. Various filters formed for this purpose are known.
In a general manner, by virtue of such filters, (called “vertical loops”), the estimated vertical speed is obtained by the integration of the sum:                of a first component corresponding to a vertical acceleration measurement, and        of a second component obtained from the difference between a first value incorporating a barometric measurement (barometric altitude or barometric vertical speed) and a second value incorporating (directly or after integration) a previous estimation of said vertical-speed.        
Although they make it possible to reduce the errors in the estimation of the vertical speed of the aircraft, such filters do not give rise to a sufficient error reduction as to allow the use of this estimation at low altitude. Furthermore, as the pilot uses the vertical speed measurement as piloting reference and as the errors are spread over time, the piloting errors stemming therefrom could be very considerable and highly consequential. In particular, an underestimated speed would have the consequence of prompting the pilot to increase the speed with the risk of reaching the aircraft's power limit and of exiting the permitted flight domain.